Local primordial non-Gaussian bias from time evolution

Primordial non-Gaussianity (PNG) is a signature of fundamental physics in the early Universe that is probed by cosmological observations. It is well known that the local type of PNG generates a strong signal in the two-point function of large-scale structure tracers, such as galaxies. This signal, often termed ``scale-dependent bias'' is a generic feature of modulation of gravitational structure formation by a large-scale mode. It is less well appreciated that the coefficient controlling this signal, ${b}_{\ensuremath{\phi}}$, is closely connected to the time evolution of the tracer number density. This correspondence between time evolution and local PNG can be simply explained for a universal tracer whose mass function only depends on peak height and, more generally, for nonuniversal tracers in the separate universe picture, which we validate in simulations. We also describe how to recover the bias of tracers subject to a survey selection function and perform a simple demonstration on simulated galaxies. Since the local PNG amplitude in $n$-point statistics (${f}_{\mathrm{NL}}$) is largely degenerate with the coefficient ${b}_{\ensuremath{\phi}}$, this proof of concept study demonstrates that Galaxy survey data can allow for more optimal and robust extraction of local PNG information from upcoming surveys.